MATHEMATICS HIGH SCHOOL

N=480×10^9
Write N as a product of powers of its prime factors.

Answers

Answer 1

Answer:

N = 5^(10) × 2^(14) × 3

This is about prime factors

By definition, a prime factor is a factor of a number and that factor is also a prime number.

A prime number is one that is divisible by only itself and 1.

The number we have is; 480 × 10^(9)

Now, let's list the prime factors or 480 and they are;

2, 3, 5

Now, using these prime factors alone to get 480, we have;

5 × 3 × 2 × 2 × 2 × 2 × 2 = 480

In powers, gives;

5 × 3 × 2^(5)

Now,the 10^(9) with the 480 can also be expressed in terms of it's prime factors which are 2 and 5 as;

(5 × 2)^(9)

Expanding this gives; 5^(9) × 2^(9) = 10^(9)

Thus;

480 × 10^(9) = 5 × 3 × 2^(5) × 5^(9) × 2^(9)

This gives;

5^(10) × 2^(14) × 3

Read more at; brainly.com/question/4853862

Answer 2

Answer:

Answer:

I got 5^10 x 2^14 x 3

Step-by-step explanation:

1. Do a tree to find 480 as a product of its prime factors

2. You should get 480= 5x2x3x2x2x2x2

3. 10 expressed as a product of its prime factors is 5x2

4. so 10^9 expressed as a product of its prime factors would be

5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2

5. You can then write out 480x10^9 as a product of its prime factors

5x2x3x2x2x2x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2x5x2

6. change this to use powers

5^10 x 2^14 x 3

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A farmer uses a lever to move a large rock. The force required to move the rock varies inversely with the distance from the pivot to the point the force is applied. A force of 50 pounds applied to the lever 36 inches from the pivot point of the lever will move the rock. Which function models the relationship between f, the amount of force applied to the lever and d the distance of the applied force from the pivot point?

Answers

Answer:f=1800/d Inverse proportion function. Provided f is in pounds & d is in inches.

Step-by-step explanation: the relationship between f & d is inverse proportion.

A constant k has to be derived from the relationship.

If f is inversely proportional to d then f=k(1/d)

K= f X d

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The doubling time of a population of grasshoppers is 10 days. By what factor does the population of grasshoppers grow in 35 days?

Answers

so in 10 days the grasshopper (x) is doubled (2x)
20 days it is 2(2x) or 4x
30 days it is 2(4x) or 8x
in 35 days it is 1/2 of 10 so 1/2 times 2 times 8x=8x

it increased by a factor of 8

The correct answer is:

11.3

Explanation:

In 10 days, the population x would double, becoming 2x.

Every 10 days after, the population would double again. This means at 20 days, the population would be 2(2x) = 4x, and at 30 days, the population would be 2(4x) = 2(2(2x)) = 8x.

Writing the repeated multiplication out, we see that this can be represented with exponents. 10 days would be 2¹(x); 20 days would be 2²(x); 30 days would be 2³(x).

5 days would not be adding a whole number to the exponent, as it is only half of the time it takes to double. This means we would add 0.5 to the exponent; this would make 35 days

$2^(3.5)(x)$ , which comes out to 11.3x. This means it increases by a factor of 11.3 in 35 days.

What is the slope of the line y = 2x + 1 ?

Answers

y = 2x + 1

The slope of the line y is 2.

In the formula: y = mx + b

m is the slope while b is the y-intercept. Since 2 is the number that is in the place of m, it is the slope of the line while 1 is the y-intercept.

y=mx+b

M is the slope, and B is the Y-intercept.

y=2x+b

In this case, 2 is m.

The slope is 2/1, or 2.

I hope I helped! :)

The minimum of the graph of a quadratic function is located at (–1, 2). The point (2, 20) is also on the parabola. Which function represents the situation?A.f(x) = (x + 1)2 + 2
B.f(x) = (x – 1)2 + 2
C.f(x) = 2(x + 1)2 + 2
D.f(x) = 2(x – 1)2 + 2

Answers

Minimum wykresu funkcji kwadratowej znajduje się w ( -1, 2). Punkt ( 2 , 20) jest również od paraboli. Która funkcja reprezentuje sytuację?
Canonical form of the function
f(x) = a* (x - p)² + q

A .f(x) = (x + 1)² + 2 ⇔ p= -1 , q = 2
B. f(x) = (x – 1)² + 2 we reject
C. f(x) = 2(x + 1)² + 2 ⇔ p = -1 , q = 2
D .f(x) = 2(x – 1)² + 2 we reject

The point (2,20) substitute
A f(x) = (x +1)² + 2
20 = (2 + 1 )² + 2
20 ≠ 9 +2
20 ≠ 11 we reject

D f(x) = 2* (x + 1)² + 2
20 = 2* (2+1)² + 2
20 = 2 * 3² + 2
20 = 2 * 9 + 2
20 = 18 + 2

Reply C

I’m trying to do this equation but don’t know where the 2 came from when you square it. Can somebody explain where the 2x come from? The 2x on the right side

Answers

okay so at the bottom it says square both sides so you have to square (x+1). when you do that you're basically just doing (x+1)(x+1) and you just use the foil method and end up with x^2 + 2x + 1

Find the common ratio for the following sequence. 27, 9, 3, 1, .